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If the total cost of a housing project...

by BTGmoderatorLU » Fri Oct 20, 2017 10:00 am
If the total cost of a housing project with f units is $1,750,000, what was the cost per unit for the housing project?

(1) If half as many units were built for the same total price, the cost per unit would be $250,000.
(2) If six more units had been built for the same total price, the cost per unit would be $3,750 less.

The OA is D.

i don't have it clear. Can any expret help me with this DS question please?
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Source: — Data Sufficiency |

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by [email protected] » Fri Oct 20, 2017 10:36 am
Hi LUANDATO,

We're told that the total cost of a housing project with F units is $1,750,000. We're asked for the cost per unit for the housing project. Although the question does not explicitly state the fact, we're meant to assume that each unit cost the same amount of money to build.

(1) If half as many units were built for the same total price, the cost per unit would be $250,000.

Fact 1 gives us a 'hypothetical' - with HALF as many units, and the same total price, the cost/unit would be $250,000. With this information we can calculate the number of units that would be built under this situation:
$1,750,000/$250,000 = 7 units
We're told that this would be HALF of the actual number of units, so the current number of units must be 14.
Fact 1 is SUFFICIENT

2) If six more units had been built for the same total price, the cost per unit would be $3,750 less.

With the information in the prompt, we can create the following equation:
(F units)($X per unit) = $1,750,000

With the information in Fact 2, we can create another equation:
(F+6)($X - $3,750) = $1,750,000

We now have a two variable/two equation 'system', so we CAN solve it - and there would only be one solution.
Fact 2 is SUFFICIENT

Final Answer: D

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
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